Scale and resolution effects of topographic index by 2-D continuous wavelet transform

Topographic index (TI) is an important parameter in catchment hydrology. The resolution dependence of TI statistics such as mean and variance has been discussed extensively in literature, while the TI structure at different scales, a different issue from resolution, needs more attention. To deal with the directional characteristics of TI structure, this paper uses the two-dimensional continuous wavelet transform (CWT) to explore the TI structure at different scales under several resolutions. For the 90-m resolution, the TI structure can be retrieved up to the scale of 270 m; only the main features (such as main streams) can be retrieved with the scale of 360 m; and even the main structure cannot be retrieved with the 900 m scale. For the 180 m resolution, both high and low order streams can be retrieved at the 180 scale; but for 270 m resolution, only the main steam structure can be captured at the 270 scale. Such preliminary results can give some insight into a suitable DEM resolution for deriving TI and the scale characteristics of TI structure. For example, the 180 m resolution of TI can be used if the high resolution DEM, such as 30 m resolution. is not available; the 270 m resolution TI is not suitable for capturing the flow process in the second or higher order stream.